Calculate the ratio of the resistance of 120 m of aluminum w

Calculate the ratio of the resistance of 12.0 m of aluminum wire 2.0 mm in diameter, to 30.0 m of copper wire 2.7 mm in diameter. Assume electrical resistivity of aluminum is 2.65×108 m and electrical resistivity of copper is 1.68×108 m.

Solution

R =   L /A

= resistivity of wire,

L=Length of wire,

A=Cross section area of wire = D²/4, D=Diameter of wire

R_AL/R_CU = (_AL L_AL D²_CU )/ ( _CU L_CUD²_AL ) = (2.65x10^-8 x 12 x (2.7)² ) / (1.68x10^-8 x 30 x (2.0)² ) = 1.15